syntax
DESCRIPTION
syntaxTRANSCRIPT
Syntax
*
[a,gX,perf,retcode,delta,tol] =
srchhyb(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)
Description
srchhyb is a linear search routine. It searches in a given direction to locate the minimum of the performance function in that direction. It uses a technique that is a combination of a bisection and a cubic interpolation.
srchhyb(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf) takes these inputs,
net
Neural network
X
Vector containing current values of weights and biases
Pd
Delayed input vectors
Tl
Layer target vectors
Ai
Initial input delay conditions
Q
Batch size
TS
Time steps
dX
Search direction vector
gX
Gradient vector
perf
Performance value at current X
dperf
Slope of performance value at current X in direction of dX
delta
Initial step size
tol
Tolerance on search
ch_perf
Change in performance on previous step
and returns
a
Step size that minimizes performance
gX
Gradient at new minimum point
perf
Performance value at new minimum point
retcode
Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function.
0
Normal
1
Minimum step taken
2
Maximum step taken
3
Beta condition not met
delta
New initial step size, based on the current step size
tol
New tolerance on search
Parameters used for the hybrid bisection-cubic algorithm are
alpha
Scale factor that determines sufficient reduction in perf
beta
Scale factor that determines sufficiently large step size
bmax
Largest step size
scale_tol
Parameter that relates the tolerance tol to the initial step size delta, usually set to 20
The defaults for these parameters are set in the training function that calls them. See traincgf, traincgb, traincgp, trainbfg, and trainoss.
Dimensions for these variables are
Pd
No x Ni x TS cell array
Each element P{i,j,ts} is a Dij x Q matrix.
Tl
Nl x TS cell array
Each element P{i,ts} is a Vi x Q matrix.
Ai
Nl x LD cell array
Each element Ai{i,k} is an Si x Q matrix.
where
Ni
=
net.numInputs
Nl
=
net.numLayers
LD
=
net.numLayerDelays
Ri
=
net.inputs{i}.size
Si
=
net.layers{i}.size
Vi
=
net.targets{i}.size
Dij
=
Ri * length(net.inputWeights{i,j}.delays)
Examples
Here is a problem consisting of inputs p and targets t to be solved with a network.
*
p = [0 1 2 3 4 5];
t = [0 0 0 1 1 1];
A two-layer feed-forward network is created. The network's input ranges from [0 to 10]. The first layer has two tansig neurons, and the second layer has one logsig neuron. The traincgf network training function and the srchhyb search function are to be used.
Create and Test a Network
*
net = newff([0 5],[2 1],{'tansig','logsig'},'traincgf');
a = sim(net,p)
Train and Retest the Network
net.trainParam.searchFcn = 'srchhyb';
net.trainParam.epochs = 50;
net.trainParam.show = 10;
net.trainParam.goal = 0.1;
net = train(net,p,t);
a = sim(net,p)
Network Use
You can create a standard network that uses srchhyb with newff, newcf, or newelm.
To prepare a custom network to be trained with traincgf, using the line search function srchhyb,
1. Set net.trainFcn to 'traincgf'. This sets net.trainParam to traincgf's default parameters.
2. Set net.trainParam.searchFcn to 'srchhyb'.
The srchhyb function can be used with any of the following training functions: traincgf, traincgb, traincgp, trainbfg, trainoss.
Algorithm
srchhyb locates the minimum of the performance function in the search direction dX, using the hybrid bisection-cubic interpolation algorithm described on page 50 of Scales (see reference below).
Reference
Scales, L.E., Introduction to Non-Linear Optimization, New York Springer-Verlag, 1985
See Also
srchbac, srchbre, srchcha, srchgol
regulasi falsi
Find zeros of function in given interval
Syntax
z = fnzeros(f) z = fnzeros(f,[a b])
Description
z = fnzeros(f) provides the 2-rowed matrix z that is an ordered list of the zeros of the continuous univariate spline in f in its basic interval.
z = fnzeros(f,[a b]) looks for zeros only in the interval [a .. b] specified by the input.
Each column z(:,j) contains the left and right endpoint of an interval. These intervals are of three kinds:
If the endpoints agree, then the function in f is relatively small at that point. If the endpoints agree to many significant digits, then the function changes sign across
the interval, and the interval contains a zero of the function -- provided the function is continuous there.
If the endpoints are not close, then the function is zero on the entire interval.
Examples
Example 1. We construct and plot a piecewise linear spline that has each of the three kinds of zeros, use fnzeros to compute all its zeros, and then mark the results on that graph.
sp = spmak(augknt(1:7,2),[1,0,1,-1,0,0,1]); fnplt(sp) z = fnzeros(sp) nz = size(z,2); hold on plot(z(1,:),zeros(1,nz),'>',z(2,:),zeros(1,nz),'<'), hold off
This gives the following list of zeros:
z = 2.0000 3.5000 5.0000 2.0000 3.5000 6.0000
In this simple example, even for the second kind of zero, the two endpoints agree to all places.
Example 2. We generate a spline function with many extrema and locate all that are in a certain interval by computing the zeros of the spline function's first derivative there.
rand('seed',23) sp = spmak(1:21,rand(1,16)-.5); fnplt(sp) z = mean(fnzeros(fnder(sp),[7,14])); zy = fnval(sp,z); hold on, plot(z,zy,'o'), hold off
Example 3. We construct a spline with a zero at a jump discontinuity and in B-form and find all the spline's zeros in an interval that goes beyond its basic interval.
sp = spmak([0 0 1 1 2],[1 0 -.2]); fnplt(sp) z = fnzeros(sp,[.5, 2.7]) zy = zeros(1,size(z,2)); hold on, plot(z(1,:),zy,'>',z(2,:),zy,'<'), hold off
This gives the following list of zeros:
z = 1.0000 2.0000 1.0000 2.7000
Notice the resulting zero interval [2..2.7], due to the fact that, by definition, a spline in B-form is identically zero outside its basic interval.
Algorithm
fnzeros first converts the function to B-form. It locates zero intervals by the corresponding sequence of consecutive zero B-spline coefficients. It locates the sign changes in the B-spline coefficients for the function, isolates them from each other by suitable knot insertion, and then uses the Modified Regula falsi to locate the corresponding sign changes in the function, if any.
See Also
fnmin, fnval
Cautionary Note
fnzeros may not work correctly for discontinuous functions. For example, for the discontinuous piecewise linear function provided by
sp = spmak([0 0 1 1 2 2],[-1 1 -1 1]), fnzeros(sp)
will only find the zero in (1..2), but not the zero in (0..1) nor the jump through zero at 1.
Newton rhapson
Division IQN
Divide IQ numbers
Library
tiiqmathlib in Target Support Package™ TC2 software
Description
This block divides two numbers that use the same Q format, using the Newton-Raphson technique. The resulting quotient uses the same Q format at the inputs.
Note The implementation of this block does not call the corresponding Texas Instruments™ library function during code generation. The TI function uses a global Q setting and the MathWorks code used by this block dynamically adjusts the Q format based on the block input. See About the IQmath Library for more information.
Dialog Box
See Also
Absolute IQN, Arctangent IQN, Float to IQN, Fractional part IQN, Fractional part IQN x int32, Integer part IQN, Integer part IQN x int32, IQN to Float, IQN x int32, IQN x IQN, IQN1 to IQN2, IQN1 x IQN2, Magnitude IQN, Saturate IQN, Square Root IQN, Trig Fcn IQN
Square Root IQN
Square root or inverse square root of IQ number
Library
tiiqmathlib in Target Support Package™ TC2 software
Description
This block calculates the square root or inverse square root of an IQ number and returns an IQ number of the same Q format. The block uses table lookup and a Newton-Raphson approximation.
Negative inputs to this block return a value of zero.
Note The implementation of this block does not call the corresponding Texas Instruments™ library function during code generation. The TI function uses a global Q setting and the MathWorks code used by this block dynamically adjusts the Q format based on the block input. See About the IQmath Library for more information.
Dialog Box
Function
Whether to calculate the square root or inverse square root
*
Square root (_sqrt) — Compute the square root.
*
Inverse square root (_isqrt) — Compute the inverse square root.
See Also
Absolute IQN, Arctangent IQN, Division IQN, Float to IQN, Fractional part IQN, Fractional part IQN x int32, Integer part IQN, Integer part IQN x int32, IQN to Float, IQN x int32, IQN x IQN, IQN1 to IQN2, IQN1 x IQN2, Magnitude IQN, Saturate IQN, Trig Fcn IQN
Metode secant
asecd
Inverse secant; result in degrees
Syntax
Y = asecd(X)
Description
Y = asecd(X) is the inverse secant, expressed in degrees, of the elements of X.
sech
Hyperbolic secant
Syntax
Y = sech(X)
Description
The sech function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.
Y = sech(X) returns an array the same size as X containing the hyperbolic secant of the elements of X.
Examples
Graph the hyperbolic secant over the domain
x = -2*pi:0.01:2*pi;
plot(x,sech(x)), grid on
Algorithm
sech uses this algorithm.
Definition
The secant can be defined as
Algorithm
sec uses FDLIBM, which was developed at SunSoft, a Sun Microsystems, Inc. business, by Kwok C. Ng, and others. For information about FDLIBM, see http://www.netlib.org.
asech
Inverse hyperbolic secant
Syntax
Y = asech(X)
Description
Y = asech(X) returns the inverse hyperbolic secant for each element of X.
The asech function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.
Examples
Graph the inverse hyperbolic secant over the domain .
x = 0.01:0.001:1;
plot(x,asech(x)), grid on
Definition
The hyperbolic inverse secant can be defined as
Algorithm
asech uses FDLIBM, which was developed at SunSoft, a Sun Microsystems™ business, by Kwok C. Ng, and others. For information about FDLIBM, see http://www.netlib.org.
asec
Inverse secant; result in radians
Syntax
Y = asec(X)
Description
Y = asec(X) returns the inverse secant (arcsecant) for each element of X.
The asec function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.
Examples
Graph the inverse secant over the domains and .
x1 = -5:0.01:-1;
x2 = 1:0.01:5;
plot(x1,asec(x1),x2,asec(x2)), grid on
Definition
The inverse secant can be defined as
Algorithm
asec uses FDLIBM, which was developed at SunSoft, a Sun Microsystems™ business, by Kwok C. Ng, and others. For information about FDLIBM, see http://www.netlib.org.
secd
Secant of argument in degrees
Syntax
Y = secd(X)
Description
Y = secd(X) is the secant of the elements of X, expressed in degrees. For odd integers n, secd(n*90) is infinite, whereas sec(n*pi/2) is large but finite, reflecting the accuracy of the floating point value of pi.
See Also
sec, sech, asec, asecd, asech
sec
Secant of argument in radians
Syntax
Y = sec(X)
Description
The sec function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.
Y = sec(X) returns an array the same size as X containing the secant of the elements of X.
Examples
Graph the secant over the domains and .
x1 = -pi/2+0.01:0.01:pi/2-0.01;
x2 = pi/2+0.01:0.01:(3*pi/2)-0.01;
plot(x1,sec(x1),x2,sec(x2)), grid on
The expression sec(pi/2) does not evaluate as infinite but as the reciprocal of the floating-point accuracy eps, because pi is a floating-point approximation to the exact value of .
Definition
The secant can be defined as
Algorithm
sec uses FDLIBM, which was developed at SunSoft, a Sun Microsystems, Inc. business, by Kwok C. Ng, and others. For information about FDLIBM, see http://www.netlib.org.